I got there in 53.3 days.
This was basically a continuation of my guide for the Express Outpost achievement.
Sorry, this Game Clip has been removed
I won't add a build list here because it's too big.
In general everything went very well - good or excellent status - extending the same plan from my Express Outpost guide. You'll want to add a Starport ASAP to boost the colonization rate. I did allow some visitors and trade off some excess materials and manufactured goods, e.g. medical supplies, later in the game. This allowed me to get some power upgrades and construction and driller robots.
I hit a barrier in the high 100s or early 200s when people started getting unhappy even though they were fed and hydrated. I rolled back a save and added large multidome with all sorts of equipment and that seemed to cure the morale issue.
Around population 220, I started to have a hunger issue that I could not correct because the population was growing fast and I didn't want to shut off colonists. (If I wasn't going for speed, I would have stopped colonists and then brought up food supplies before continuing.) I took a chance that status would not drop to poor before I could hit 250. I barely made it as you see in the video. Beat the deadline by 6.7 days. (Someone posted a youtube video completing this in 40 days!)
Hope this helps.
Note: Challenge achievements will not stack with 'regular' game achievements. Accordingly, the Express Dark Colony achievement for the completing Dark Moon challenge (300 colonists) in less than 70 days will not simultaneously earn you this achievement as well.